Method and/or system for estimating phase noise error

ABSTRACT

Embodiments of methods and/or systems for estimating phase error noise are disclosed.

RELATED APPLICATION

The current patent application claims priority to U.S. provisionalpatent application No. 60/632,439, filed on Dec. 2, 2004, titled“Minimal Mean Square Error-based Phase Noise Migration Method forMIMO-OFDM,” assigned to the assign of the presently claimed subjectmatter.

FIELD

This disclosure is related to communications.

BACKGROUND

It is desirable in communications to have the ability to estimate andadjust for phase error or phase noise, at least in part.

BRIEF DESCRIPTION OF THE DRAWINGS

Subject matter is particularly pointed out and distinctly claimed in theconcluding portion of the specification. Claimed subject matter,however, both as to organization and method of operation, together withobjects, features, and advantages thereof, may best be understood byreference of the following detailed description if read with theaccompanying drawings in which:

FIG. 1 is a schematic diagram illustrating an embodiment of acommunications system employing an MIMO-OFDM scheme;

FIGS. 2-5 are plots illustrating simulated performance results ofemploying various embodiments of a method of estimating phase errornoise.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth to provide a thorough understanding of claimed subject matter.However, it will be understood by those skilled in the art that claimedsubject matter may be practiced without these specific details. In otherinstances, well known methods, procedures, components and/or circuitshave not been described in detail so as not to obscure claimed subjectmatter.

Some portions of the detailed description which follow are presented interms of algorithms and/or symbolic representations of operations ondata bits and/or binary digital signals stored within a computingsystem, such as within a computer and/or computing system memory. Thesealgorithmic descriptions and/or representations are the techniques usedby those of ordinary skill in the data processing arts to convey thesubstance of their work to others skilled in the art. An algorithm ishere, and generally, considered to be a self-consistent sequence ofoperations and/or similar processing leading to a desired result. Theoperations and/or processing may involve physical manipulations ofphysical quantities. Typically, although not necessarily, thesequantities may take the form of electrical and/or magnetic signalscapable of being stored, transferred, combined, compared and/orotherwise manipulated. It has proven convenient, at times, principallyfor reasons of common usage, to refer to these signals as bits, data,values, elements, symbols, characters, terms, numbers, numerals and/orthe like. It should be understood, however, that all of these andsimilar terms are to be associated with appropriate physical quantitiesand are merely convenient labels. Unless specifically stated otherwise,as apparent from the following discussion, it is appreciated thatthroughout this specification discussions utilizing terms such as“processing”, “computing”, “calculating”, “determining” and/or the likerefer to the actions and/or processes of a computing platform, such as acomputer or a similar electronic computing device, that manipulatesand/or transforms data represented as physical electronic and/ormagnetic quantities and/or other physical quantities within thecomputing platform's processors, memories, registers, and/or otherinformation storage, transmission, and/or display devices.

For one embodiment in accordance with claimed subject matter, anMMSE-based scheme for estimating phase error noise is applied to anMIMO-OFDM communication system, such as systems with any number ofantennas. Such an embodiment, it is believed provides better performancethan what has been obtained with other phase error estimatingapproaches, such as a least squares (LS) approach, and shows robustnesswith respect to both number of antennas and SNR levels. Likewise, suchas approach may be applied independent of coding scheme, and, therefore,may be used in various applications, such as BLAST or space-time coding,for example.

The combination of OFDM modulation with multiple input multiple output(MIMO) systems, may increase the system capacity and reduce receivercomplexity, such as for time-variant and frequency-selective channels,for example. Therefore, MIMO-OFDM has become a promising candidate forhigh performance future 4G broadband wireless communications. However,similar to SISO-OFDM, MIMO-OFDM may be sensitive to the level of noise,such as phase error noise, which may result in performance degradation.

Even though various phase noise adjustment methods for single-antennasystems exist, multi-antenna communications systems have not beenwell-studied. As previously alluded to, for one embodiment, a MinimalMean Square Error (MMSE)-based approach may be applied to an MIMO-OFDMcommunication system to estimate phase error noise, although, of course,claimed subject matter is not limited in scope in this respect. Inparticular, simulation results are shown herein for 64 sub-carriers,16QAM modulation, with phase noise variance of 0.01.

A Multiple Input Multiple Output (MIMO) technique takes advantage of thediversity that may obtained by spatially separated antennas in a densemulti-path scattering environment, although claimed subject matter isnot limited in scope in this respect. However, see, for example, D.Gesbert and et al., “From theory to practice: an overview of MIMOspace-time coded wireless systems,” IEEE J. Select. Areas Commun., vol.21, pp. 281-297, April 2003 (hereinafter referred to as [1]). MIMO mayprovide a linear increase in the transmission rate (or capacity),potentially for the same bandwidth and potentially with no additionalpower expenditure. Diversity may, for example, be achieved through socalled space-time codes. See, for example, e, V. Tarokh and A. Seshadri,“Space-time codes for high data rate wireless communication: Performancecriterion and code construction,” IEEE Trans. Inform. Theory, vol. 44,pp. 744-765, March 1998 (hereinafter referred to as [2]), while high bitrates may be achieved by spatial multiplexing systems, such as thepioneer system from Bell Labs abbreviated as BLAST. See, for example P.W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela,“V-BLAST: An architecture for realizing very high data rates overrich-scattering wireless channel,” PROC. ISSSE, pp. 295-300, 1998(hereinafter referred to as [3]). However, again, claimed subject matteris not limited in scope to these illustrative system examples.

Orthogonal frequency division multiplexing (OFDM) is an attractivemodulation scheme used in broadband wireless systems which encounterlarge delay spread, for example, although, again, claimed subject matteris not limited in scope in this respect. Nonetheless, see, for example,Z. Wang and G. B. Giannakis, “Wireless multicarrier communications:Where fourier meets Shannon,” Signal Processing Magazine, IEEE, vol. 17,pp. 29-48, May 2000 (hereinafter [4]); “OFDM or single-carrier blocktransmission?” Transaction or Communication, IEEE, vol. 52, pp. 380-394,March 2004 (hereinafter [5]). Thus, OFDM has been adopted in a varietyapplications, e.g., digital subscriber line (DSL), digital video/audiobroadcasting (DVB/DAB), IEEE 802.11a wireless local area network(HIPERLAN/2); see, for example, J. Bingham, “Multicarrier modulation fordata transmission: an idea for whose time has come,” IEEE Commun. Mag.,vol. 28, pp. 5-14, May 1990(hereinafter [6]); IEEE Std 802.11a-1999,Supplement to IEEE standard for informationtechnology—telecommunications and information exchange betweensystems—local and metropolitan area networks—specific requirements. Part11; wireless LAN medium access control (MAC) and physical layer (PHY)specifications; high-speed physical layer in the 5 GHz band.http://www.ieee.org. December 1999 (hereinafter [7]).

A principle of OFDM is to convert a frequency-selective channel into aparallel collection of frequency flat sub-channels. The signal may thenbe recovered by a one-tap equalizer on each flat sub-channel, forexample. Since the different subcarriers overlap in frequency, theavailable bandwidth is used efficiently.

A combined MIMO-OFDM scheme has an advantage over conventional systemsat least in part due to its improved system capacity of BER performanceintroduced by MIMO technique, and its robustness to channel frequencyselectively due at least in part to an OFDM technique. However, similarto OFDM, MIMO-OFDM suffers performance degradation due at least in partto the presence of phase noise. As previously suggested, in oneembodiment, an MMSE-based approach to estimating phase error may beemployed to improve system performance, such as may be employed at areceiver or by a computing device incorporated in a receiver, forexample. Although, again, claimed subject matter is not limited in scopeto these particular embodiments.

Consider a frequency selective MIMO channel with M_(T) (also denoted MTherein) transmit antennas and M_(R) (also denoted MR herein) receiveantennas. The channel on sub-carrier k may be represented by M_(R)×M_(T)matrix H(k). Define X=[X₁, X₂, . . . , X_(MT)]^(T)=[X(0), X(1), . . . ,X(N−1)] as a M_(T)-by-N matrix which comprises transmitted data for onesymbol duration T, where X_(t)=[X_(t)(0), X_(t)(1), . . . X_(t)(N−1]^(T)denotes a transmitted OFDM symbol on t-th antenna, and X(k)=[X₁(k),X₂(k), . . . , X_(MT)(k)]^(T) denotes transmitted data for the antennason sub-carrier k, which is between 0 and N−1. The IDFT of the data blockon a transmit antenna yields the time domain sequence x_(t)=[x_(t)(0),x_(t)(1), . . . x_(t)(N−1)]^(T). After inserting Cyclix prefix (CP)which is assumed to be greater than the channel length, the sequence istransmitted over the transmit antennas. At the receive antennas, the CPis stripped off and data is fed into a DFT unit. By using CP in the datasequence, the time domain linear convolution is equivalent to cyclicconvolution. Assume Y=[Y₁, Y₂, . . . , Y_(MR)]^(T)=[Y(0), Y(1), . . .Y(N−1)] denotes received data from an antenna, whereY_(r)=[Y_(r)(0)Y_(r)(1), . . . , Y_(r)(N−1)] ^(T) denotes a receivedOFDM symbol on r-th antenna, and Y(k)=[Y₁(k), Y₂(k), . . . ,Y_(MR)(k)]^(T) denotes the received signal on k-th sub-carrier. Hence,the general form of an MIMO-OFDM process may be summarized as:

$\begin{matrix}{{Y(k)} = {{\sqrt{\frac{E_{S}}{M_{T}}}{H(k)}{X(k)}} + {N(k)}}} & (1)\end{matrix}$where E_(s) is the average energy allocated to the k-th sub-carrierevenly divided across the transmit antennas, H(k) is a M_(R)×M_(T)matrix which is given by:

${H(K)} = \begin{bmatrix}{H_{11}(k)} & {H_{12}(k)} & \ldots & {H_{1M_{T}}(k)} \\{H_{21}(k)} & {H_{22}(k)} & \ldots & {H_{2M_{T}}(k)} \\\vdots & \vdots & \ddots & \vdots \\{H_{M_{R}1}(k)} & {H_{M_{R}2}(k)} & \ldots & {H_{M_{R}M_{T}}(k)}\end{bmatrix}$and N(k)=[N₁(k), N₂(k), . . . , N_(MR)(k)]^(T) denotes the noise onsub-carrier k which are zero-mean AWGN with the variance σ² _(N).

Several space-time coding techniques have been proposed, such asdiscussed in previously cited [2], and later were extended to the OFDMfield. Of course, claimed subject matter is not limited to a particularcoding scheme. Another interesting approach is space-frequency codingtechnique, introduced in Lee and Williams, “A space-frequencytransmitter diversity technique for ofdm systems,” GLOBECOM'00 (SanFrancisco, Calif.), vol. 3, pp. 1473-1477, November 2000, (hereinafter[8]) with 2×1 (M_(T)=2, M_(R)=1) antennas, which is the frequency domaincounterpart of Alamouti's space-time coding technique, see Alamouti, “Asimple transmitter diversity scheme for wireless communications,” IEEEJ. Select. Areas Commun., Vol. 16, pp 1451-1458, October 1998(hereinafter [9]). Following the same method as in [8], the effect ofphase noise using a 2×2 scenario is shown in FIG. 1. In order toimplement the transmit diversity technique in [8], for example, X₁ andX₂ are encoded in bits as:X ₁ =[X(0),−X*(1), . . . ,X(N−2),−X*(N−1)]^(T)  (2)X ₂ =[X(1),X*(0), . . . ,X(N−1),X*(N−2)]^(T)  (3)For the sake of simplicity, we assume

$\sqrt{\frac{E_{s}}{M_{t}}} = 1.$Hence from (1), the scalar form for A 2×2 case is given by:

$\begin{matrix}\begin{matrix}{{Y_{r}(k)} = {{\sum\limits_{t = 1}^{2}{{H_{tr}(k)}{X_{t}(k)}}} + {N_{r}(k)}}} & {{r = 1},2}\end{matrix} & (4)\end{matrix}$where X_(t)(k) is the (k+1)th element of X_(t).

The space-frequency transmit diversity technique [8] involves A fadingchannel on adjacent sub-carriers BEING approximately constant. Thiscondition holds in cases if channel coherent bandwidth is relativelylarge compared with transmission bandwidth. This is not as stringent asin space-time block coding, which has a fading channel on adjacent OFDMsymbols as constant.

Without loss of generality, the 2k and (2k+1)th frequency-domaindata(sub-carrier) signal pair is studied. The space-frequency decodingof this signal pair is simply given by the same combining scheme in [9].Assume no phase noise exists, the combining rules are given by:

$\begin{matrix}{{\hat{X}\left( {2k} \right)} = {{{{Y_{1}\left( {2k} \right)}{H_{11}^{*}\left( {2k} \right)}} + {{Y_{1}^{*}\left( {{2k} + 1} \right)}{H_{21}\left( {2k} \right)}} + {{Y_{2}\left( {2k} \right)}{H_{12}^{*}\left( {2k} \right)}} + {{Y_{2}^{*}\left( {{2k} + 1} \right)}{H_{22}\left( {2k} \right)}}} = {{{X\left( {2k} \right)}{\sum\limits_{t = 1}^{2}{\sum\limits_{r = 1}^{2}{{H_{tr}\left( {2k} \right)}}^{2}}}} + {{H_{11}^{*}\left( {2k} \right)}{N_{1}\left( {2k} \right)}} + {{H_{21}\left( {2k} \right)}{N_{1}^{*}\left( {{2k} + 1} \right)}} + {{H_{12}^{*}\left( {2k} \right)}{N_{2}\left( {2k} \right)}} + {{H_{22}\left( {2k} \right)}{N_{2}^{*}\left( {{2k} + 1} \right)}}}}} & (5) \\{{\hat{X}\left( {{2k} + 1} \right)} = {{{{Y_{1}\left( {2k} \right)}{H_{11}^{*}\left( {2k} \right)}} - {{Y_{1}^{*}\left( {{2k} + 1} \right)}{H_{21}\left( {2k} \right)}{Y_{2}\left( {2k} \right)}{H_{12}^{*}\left( {2k} \right)}} - {Y_{2}*2\left( {{2k} + 1} \right){H_{22}\left( {2k} \right)}}} = {{{X\left( {{2k} + 1} \right)}{\sum\limits_{t = 1}^{2}{\sum\limits_{r = 1}^{2}{{H_{tr}\left( {2k} \right)}}^{2}}}} + {{H_{21}^{*}\left( {2k} \right)}{N_{1}\left( {2k} \right)}} - {{H_{11}\left( {2k} \right)}{N_{1}^{*}\left( {{2k} + 1} \right)}} + {{H_{22}^{*}\left( {2k} \right)}{N_{2}^{*}\left( {2k} \right)}} - {{H_{12}\left( {2k} \right)}{N_{2}^{*}\left( {{2k} + 1} \right)}}}}} & (6)\end{matrix}$The space diversities provided by both transmit and receive antennas areexploited by this combining scheme.

In this context, the term phase noise is used for describing short termrandom frequency fluctuations of a signal. It may result fromtransmitter and receiver oscillators and may be described as acontinuous Brownian motion process with zero mean and variance 2πβt,where β denotes the phase noise linewidth, although claimed subjectmatter is not limited in scope in this respect. By including phase noiseeffect, the expression of (4) is subsequently modified to:

$\begin{matrix}{{Y_{r}(k)} = {{\sum\limits_{t = 1}^{2}{{H_{tr}(k)}{X_{t}(k)}{C(0)}}} + {\sum\limits_{t = 1}^{2}\underset{\underset{{ICI}_{tr}{(k)}}{︸}}{\sum\limits_{{n = 0},{n \neq k}}^{N - 1}{{H_{tr}(n)}{X_{t}(n)}{C\left( {n - k} \right)}}}} + {N_{r}(k)}}} & (7)\end{matrix}$where

${C(n)} = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{\mathbb{e}}^{{j\; 2\;{\pi k}\; n} + {j\; 0{(k)}}}}}$with o(k) denoting the phase noise. The variance of o(k) is given by2πβT, where β and T denote the phase noise linewidth and the OFDM symbolduration respectively. It is noticed from (7) that phase, noisecontributes to

-   1. Common phase error (CPE), indicated by C(0), which may result in    the rotation of the desired signals;-   2. Intercarrier interference (ICI), indicated by the term    ICI_(t)(k), which may result in interference on the desired signals.

With medium to small phase noise levels, post-DFT phase noise adjustmentmay in particular situations be possible. Typically, CPE amounts to over90% phase noise energy while ICI is relatively small in comparison toCPE. That is, for frequency-domain correction, even though consideringboth CPE and ICI would yield better result, CPE correction may amount tothe major performance loss due to phase noise. Furthermore, the spatialdiversity provided by MIMO may also improve CPE estimator performance.Therefore, this particular embodiment addresses CPE, although, ofcourse, claimed subject matter is not limited in scope to CPEestimation.

To mitigate CPE, (7) can be rewritten as

${Y_{r}(k)} = {{\sum\limits_{t = 1}^{2}{{H_{tr}(k)}{X_{t}(k)}{C(0)}}} + {N_{r}(k)}}$where Ń_(r)(k) denotes

$\sum\limits_{t = 1}^{2}\sum\limits_{{n = 0},{n \neq k}}^{N - 1}$H_(tr)(n)X_(t)(n)C(n−k)+N_(r)(k). Define N_(p) as a number of pilotswithin an OFDM symbol, and {k₁, k₂, . . . , k_(Np)} as the correspondingpilot set. Then the pilot art of the received signal in (8) isequivalent to (9) and (10) below:

$\overset{\_}{Y} = {{{SC}(0)} + \overset{\overset{\_}{\prime}}{N}}$$\begin{matrix}{\overset{\_}{Y} = \left\lbrack {{Y_{1}(k)},{Y_{2}\left( k_{1} \right)},\ldots\mspace{14mu},{Y_{1}\left( k_{N_{p}} \right)},{Y_{2}\left( k_{N_{p}} \right)}} \right\rbrack^{T}} \\{S = \left\lbrack {{S_{1}\left( k_{1} \right)},{S_{2}\left( k_{1} \right)},\ldots\mspace{11mu},{S_{1}\;\left( k_{N_{p}} \right)},{S_{2}\left( k_{N_{p}} \right)}} \right\rbrack^{T}} \\{\overset{\overset{\_}{\prime}}{N} = \left\lbrack {{{\overset{\prime}{N}}_{1}\left( k_{1} \right)},{{\overset{\prime}{N}}_{2}\left( k_{1} \right)},\ldots\mspace{11mu},{{\overset{\prime}{N}}_{1}\;\left( k_{N_{p}} \right)},{{\overset{\prime}{N}}_{2}\left( k_{N_{p}} \right)}} \right\rbrack^{T}}\end{matrix}$${S_{r}\left( k_{p} \right)} = {{\sum\limits_{t = 1}^{2}{{H_{tr}\left( k_{p} \right)}{X_{t}\left( k_{p} \right)}\mspace{31mu} 1}} \leq p \leq N_{p}}$For this particular embodiment, phase error may be estimated byestimating C(0). This may be accomplished here by finding an appropriatecoefficient vector W which minimizes E[∥C(0)−W^(H) Y∥². With somealgebraic manipulation, it is readily shown that this coefficient hereis given by:

$\begin{matrix}{W = {\left( {{ss}^{H} + {\frac{\sigma^{2}}{E_{c}}I}} \right)^{- 1}S}} & (11)\end{matrix}$which gives rise to the MMSE estimate of CPE:

$\begin{matrix}{{\hat{C}(0)} = {{w^{h}\overset{\_}{Y}} = {{S^{H}\left( {{SS}^{H} + {\frac{\sigma^{2}}{E_{c}}I}} \right)}^{- 1}\overset{\_}{Y}}}} & (12)\end{matrix}$where E_(C) denotes the average energy of C(0), an σ² denotes thevariance of N_(r)(k). Assuming perfect knowledge of the phase noiselinewidth and channel response, and the OFDM subcarrier signals aremutually independent random variables with zero mean and variance E_(x).Then the statistics of E_(C) and N_(r)(k) are shown to be:

$\begin{matrix}{E_{c} = {{E\left\lbrack {{C(0)}}^{2} \right\rbrack} = {1 - \frac{\pi\;\beta\; T}{3}}}} & (13)\end{matrix}$

$\quad\begin{matrix}\begin{matrix}{\sigma^{2} = {{{VAR}\;\left\lbrack {{\overset{\prime}{N}}_{r}(k)} \right\rbrack} = {{\sum\limits_{t = 1}^{2}{E\left\lbrack {{{ICI}_{tr}(k)}}^{2} \right\rbrack}} + \sigma_{N}^{2}}}} \\{= {\frac{2\pi\;\beta\;{TE}_{x}}{3} + \sigma_{N}^{2}}}\end{matrix} & (14)\end{matrix}$where we assumed channel response is normalized and phase noise isindependent to AWGN. Note that larger number of pilots N_(p) increasesthe size of vector W, and improves the estimation accuracy. Spacialdiversity is exploited in this scheme, since the length of W will reduceto half in single antenna systems.

When considering the CPE effect of phase noise, the decision results in(5) and (6) are modified by multiplying the corresponding channelresponses by C(0). Then after estimation of CPE, we have:

$\begin{matrix}{{\hat{X}\left( {2k} \right)} = {{{X\left( {2k} \right)}{{\hat{C}(0)}}^{2}{\sum\limits_{t = 1}^{2}{{\sum\limits_{r = 1}^{2}}^{2}{{H_{tr}\left( {2k} \right)}}^{2}}}} + {\hat{C}*{(0)\left\lbrack {{{H_{11}^{*}\left( {2k} \right)}{N_{1}\left( {2k} \right)}} + {{H_{21}\left( {2k} \right)}{N_{1}^{*}\left( {{2k} + 1} \right)}}} \right\rbrack}} + {\hat{C}*{(0)\left\lbrack {{{H_{12}^{*}\left( {2k} \right)}{N_{2}\left( {2k} \right)}} + {{H_{22}\left( {2k} \right)}{N_{2}^{*}\left( {{2k} + 1} \right)}}} \right\rbrack}}}} & (15) \\{{\hat{X}\left( {{2k} + 1} \right)} = {{{X\left( {{2k} + 1} \right)}{{\hat{C}(0)}}^{2}{\underset{t = 1}{\sum\limits^{2}}{\sum\limits_{r = 1}^{2}{{H_{tr}\left( {2k} \right)}}^{2}}}} + {\hat{C}*{(0)\left\lbrack {{{H_{21}^{*}\left( {2k} \right)}{N_{1}\left( {2k} \right)}} - {{H_{11}\left( {2k} \right)}{N_{1}^{*}\left( {{2k} + 1} \right)}}} \right\rbrack}} + {\hat{C}*{(0)\left\lbrack {{{H_{22}^{*}\left( {2k} \right)}{N_{2}\left( {2k} \right)}} - {{H_{12}\left( {2k} \right)}{N_{2}^{*}\left( {{2k} + 1} \right)}}} \right\rbrack}}}} & (16)\end{matrix}$

As suggested previously, simulations were carried out for the IEEE802.11a standard, with 64 sub-carriers for an OFDM symbol, and thespace-frequency diversity technique was applied, wherein 16QAMmodulation is used. The length of cyclic prefix is assumed to be largerthan channel delay spread.

FIG. 2 shows the SER performance of an embodiment of a method ofestimating phase error noise in comparison to no-phase-noise andphase-noise-without-correction cases. Even for small phase noise of 10⁻²with no correction, there is an apparent error floor. On the other hand,the particular embodiment applied here mitigates phase noise andperformance therefore stays close to no-phase-noise case. Notice thateven an ML-based scheme is 1-2 dB worse than the particular embodiment.

Effect of different modulation on the proposed scheme is evaluated inFIG. 3, which shows that this particular embodiment is robust for commonmodulation methods. Also notice that the performance difference betweenan embodiment and no-phase-noise case becomes larger when theconstellation size increases, as the larger constellation is moresensitive to estimation errors.

FIG. 4 shows the effect of a number of pilots and phase noise level, onthe SER performance of the system. From this figure, we conclude thatchoosing 4 pilots gives adequate performance with high spectralefficiency (4/64=6.25% transmission bandwidth for pilots) and relativelylow computational complexity.

Finally, in FIG. 5, the normalized MMSE (NMMSE) is used to compare theperformance with different N_(p). Notice that although we can improvethe estimation error, NMMSE, by larger N_(p), the same amountimprovement does not occur for SER, as it is shown in FIG. 4.

It is worth noting that embodiments of claimed subject matter may beemployed in a variety of contexts and claimed subject matter is notlimited in scope in this respect. For example, embodiments may beemployed in a variety of possible communication devices, including, forexample, cell phones, personal digital assistants, laptop computers,media players, and the like. Of course, claimed subject matter is notlimited in scope to this example. Many other approaches and/or othertypes of devices employing a variety of software, firmware and/orhardware are possible and included within the scope of claimed subjectmatter.

It will, of course, be understood that, although particular embodimentshave just been described, the claimed subject matter is not limited inscope to a particular embodiment or implementation. For example, oneembodiment may be in hardware, such as implemented to operate on adevice or combination of devices, for example, whereas anotherembodiment may be in software. Likewise, an embodiment may beimplemented in firmware, or as any combination of hardware, software,and/or firmware, for example. Likewise, although claimed subject matteris not limited in scope in this respect, one embodiment may comprise oneor more articles, such as a storage medium or storage media. Thisstorage media, such as, one or more CD-ROMs and/or disks, for example,may have stored thereon instructions, that when executed by a system,such as a computer system, computing platform, or other system, forexample, may result in an embodiment of a method in accordance withclaimed subject matter being executed, such as one of the embodimentspreviously described, for example. As one potential example, a computingplatform may include one or more processing units or processors, one ormore input/output devices, such as a display, a keyboard and/or a mouse,and/or one or more memories, such as static random access memory,dynamic random access memory, flash memory, and/or a hard drive. Forexample, a display may be employed to display one or more queries, suchas those that may be interrelated, and or one or more tree expressions,although, again, claimed subject matter is not limited in scope to thisexample.

In the preceding description, various aspects of claimed subject matterhave been described. For purposes of explanation, specific numbers,systems and/or configurations were set forth to provide a thoroughunderstanding of claimed subject matter. However, it should be apparentto one skilled in the art having the benefit of this disclosure thatclaimed subject matter may be practiced without the specific details. Inother instances, well known features were omitted and/or simplified soas not to obscure the claimed subject matter. While certain featureshave been illustrated and/or described herein, many modifications,substitutions, changes and/or equivalents will now occur to thoseskilled in the art. It is, therefore, to be understood that the appendedclaims are intended to cover all such modifications and/or changes asfall within the true spirit of claimed subject matter.

1. A method of reducing phase error noise for a receiver employing anMIMO-OFDM scheme comprising: obtaining, at the receiver, a minimummean-square error (MMSE) estimate of common phase error; and adjusting areceived signal for a common phase error component of phase noise basedon the MMSE estimate of common phase error, wherein said obtainingcomprises estimating one or more statistics of said common phase errorand using the one or more statistics to form the MMSE estimate.
 2. Themethod of claim 1, wherein said adjusting a received signal comprisesadjusting decoding of said received signal.
 3. The method of claim 1,wherein said MIMO-OFDM scheme employs space-time coding.
 4. An apparatuscomprising: a receiver employing an MIMO-OFDM scheme; said receiveradapted to form a minimum mean-square error (MMSE) estimate of commonphase error and further adapted to adjust a received signal for a commonphase error component of phase noise based on said MMSE estimate ofcommon phase error, and wherein said receiver is further adapted toestimate one or more statistics of said common phase error and to formsaid MMSE estimate based on the one or more statistics.
 5. The apparatusof claim 4, wherein said receiver is further adapted to adjust decodingof the received signal.
 6. The apparatus of claim 4, wherein saidreceiver is adapted to receive a signal that employs space-time coding.7. The apparatus of claim 4, wherein said receiver is substantiallycompliant with aspects of IEEE 802.11.
 8. The apparatus of claim 4,wherein said receiver is incorporated in at least one of the following:a cell phone; a personal digital assistant; a laptop computer; a mediaplayer device.
 9. An apparatus comprising: a computing device; saidcomputing device adapted to form a minimum mean-square error (MMSE)estimate of common phase error for an MIMO-OFDM communication scheme,wherein said computing device is further adapted to process receivedsignals so as to adjust for a common phase error component of phaseerror noise based on said MMSE estimate of common phase error, andwherein said computing device is further adapted to estimate one or morestatistics of said common phase error and to form said MMSE estimatebased on the one or more statistics.
 10. The apparatus of claim 9,wherein said computing device is further adapted to adjust decoding ofreceived signals.
 11. The apparatus of claim 9, wherein said computingdevice is adapted to operate on signals that employ space-time coding.12. The apparatus of claim 9, wherein said computing device issubstantially compliant with aspects of IEEE 802.11.
 13. The apparatusof claim 9, wherein said computing device is incorporated in at leastone of the following: a cell phone; a personal digital assistant; alaptop computer; a media player device.
 14. An apparatus including acomputer-readable storage medium having stored thereon instructionsthat, upon execution by a computing device associated with theapparatus, cause the apparatus to perform actions comprising: obtaininga minimum mean-square error (MMSE) estimate of common phase errorassociated with a received multiple-input multiple-output orthogonalfrequency-division multiplex (MIMO-OFDM) signal; and adjusting thereceived signal for a common phase error component of phase noise basedon the MMSE estimate of common phase error, wherein said obtainingcomprises estimating one or more statistics of said common phase errorand forming the MMSE estimate using the one or more statistics.
 15. Theapparatus of claim 14, wherein said MIMO-OFDM scheme employs space-timecoding.